






'''simple docstring'''




from __future__ import annotations

def    __lowercase		(     __lowercase			)			->		int:

      '''simple docstring'''


      _A     	=      len(UpperCamelCase__			) // 2

      # choose the middle 3 elements
      _A     	=      lst[m - 1 : m + 2]

      # if middle element is peak
      if three[1] > three[0] and three[1] > three[2]:
            return three[1]

      # if increasing, recurse on right
      elif three[0] < three[2]:
            if len(lst[:m]			) == 2:
                  m -= 1
            return peak(lst[m:]			)

      # decreasing
      else:
            if len(lst[:m]			) == 2:
                  m += 1
            return peak(lst[:m]			)


if __name__ == "__main__":
    import doctest

    doctest.testmod()






'''simple docstring'''




def __lowerCAmelCase					(				UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							)      ->       int:

    def count_of_possible_combinations(UpperCamelCase__							) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        return sum(count_of_possible_combinations(target - item							) for item in array							)

    return count_of_possible_combinations(UpperCamelCase__							)






def __lowerCAmelCase					(				UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							)      ->       int:

    def count_of_possible_combinations_with_dp_array(
        UpperCamelCase__							,    UpperCamelCase__							) -> int:
        if target < 0:
            return 0
        if target == 0:
            return 1
        if dp_array[target] != -1:
            return dp_array[target]
        __lowerCamelCase            =    sum(
            count_of_possible_combinations_with_dp_array(target - item							,    UpperCamelCase__							)
            for item in array							)
        __lowerCamelCase            =    answer
        return answer

    __lowerCamelCase            =    [-1] * (target + 1)
    return count_of_possible_combinations_with_dp_array(UpperCamelCase__							,    UpperCamelCase__							)






def __lowerCAmelCase					(				UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							)      ->       int:
    __lowerCamelCase            =    [0] * (target + 1)
    __lowerCamelCase            =    1

    for i in range(1							,    target + 1							):
        for j in range(UpperCamelCase__							):
            if i - array[j] >= 0:
                dp_array[i] += dp_array[i - array[j]]

    return dp_array[target]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __UpperCAmelCase					=3
  __UpperCAmelCase					=5
  __UpperCAmelCase					=[1, 2, 5]
  print(combination_sum_iv(n, array, target))
